Question: The sum of two numbers is $58$, and their difference is $4$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 58}$ ${x-y = 4}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 62 $ $ x = \dfrac{62}{2} $ ${x = 31}$ Now that you know ${x = 31}$ , plug it back into $ {x+y = 58}$ to find $y$ ${(31)}{ + y = 58}$ ${y = 27}$ You can also plug ${x = 31}$ into $ {x-y = 4}$ and get the same answer for $y$ ${(31)}{ - y = 4}$ ${y = 27}$ Therefore, the larger number is $31$, and the smaller number is $27$.